The volume of the sphere is 32 cubic cm
The formula to find the volume of the cylinder: -
[tex]V=\pi \times r^{2}\times h[/tex]
where, r is the radius of cylinder and 'h' is the height of the cylinder
The formula to find the volume of the sphere: -
[tex]V=\frac{4}{3}\times \pi \times r^3[/tex]
where, r is the radius of the sphere
We have been given that a sphere and a cylinder have the same radius and height.
This means, diameter of the sphere = height of the cylinder
Let, 'h' represents the height of the cylinder and 'r' represents the radius of the sphere.
⇒ h = 2r
Also, the volume of the cylinder = 48 cubic cm
Let [tex]V_{s},V_c[/tex] represent the volume of the sphere and the cylinder respectively.
Consider the volume of the cylinder,
⇒ [tex]V_c = 48[/tex]
⇒ [tex]\pi \times r^2 \times h =48[/tex]
⇒ [tex]\pi \times r^2 \times 2r=48[/tex] ..................(Since h = 2r)
⇒ [tex]\pi \times r^3 = 24[/tex] ...................(1)
Now, the volume of the sphere would be,
⇒ [tex]V_s=\frac{4}{3} \times \pi \times r^3[/tex]
⇒ [tex]V_s=\frac{4}{3} \times 24[/tex]
⇒ [tex]V_s=32[/tex] cubic cm
Therefore, the volume of the sphere is 32 cubic cm.
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